Roger Federer began the defence of his Indian Wells title with a 6-3 6-3 win over American Mardy Fish on Sunday.
The world number one, who is seeking his 26th career singles title, will now face either Gilles Muller or Radek Stepanek in the third round.
Australia's second seed Lleyton Hewitt beat American Robby Ginepri 6-2 7-6 and Carlos Moya downed fellow Spaniard Juan Carlos Ferrero 6-3 6-4.
Australian Open winner Marat Safin beat Finland's Jarkko Nieminen 4-6 6-1 7-5.
"We'll really see after these two events, Indian Wells and Miami, how I'm really shaping up, if I'm still number one in the race," Federer said.
"But so far I have the feeling that the chances are there to repeat last year's season."
In other action, France's Paul-Henri Mathieu surprised Tommy Haas 7-6 (7-3) 6-3 and France's Fabrice Santoro beat 11th seed Joachim Johansson, of Sweden, 4-6 6-2 7-6 (8-6).
Croatia's Davis Cup star Ivan Ljubicic won 6-3 6-2 against Czech Tomas Zib, while another Croatian, Mario Ancic, lost 7-5 3-6 6-2 to Czech Tomas Berdych.